Find the points of discontinuity for the following functions: (i) f(z) = (z+z+0)/(z+7) (ii) g(z) = (z2−4)/(z-1) (iii) h(z) = (z+2)(z+1)/(z+2)

$f(z) = (2z)/(z+7)$

$z+7 = 0$
$z = -7$

• The point of discontinuity for $f(z)$ is z = -7.

2) Function (ii): $g(z) = (z²-4)/(z-1)$

$z-1 = 0$
$z = 1$

• The point of discontinuity for $g(z)$ is z = 1.

3) Function (iii): $h(z) = (z+2)(z+1)/(z+2)$

$z+2 = 0$
$z = -2$

Even though you could simplify this function by canceling out $(z+2)$ from the top and bottom (making it $h(z) = z+1$), the original function is still undefined at $z = -2$ because it would make the denominator zero. So, there's a "hole" in the graph at that point.

• The point of discontinuity for $h(z)$ is z = -2.